Efficient Material Model Calibration using EDEM, romAI and HyperStudy
Altair Employee1.0 Introduction
Material model calibration is critical to accurate Discrete Element Method (DEM)-based modeling of granular materials. This article demonstrates an efficient workflow for material model calibration that combines Altair EDEMTM with machine learning through Altair HyperStudy (HST)TM, and Altair romAITM. Figure 1 outlines this workflow. Considering the FT4 Rheometer as an example, this article presents an approach that can leverage romAIfor efficient material calibration.
A Rheometer test is used to evaluate the flowability of bulk materials under dynamic flow conditions (more on the FT4 Rheometer can be accessed here). Powder flowability/ rheology is deduced from a Rheometer test's temporal evolution of force and torque curves. The primary objective of this work is to predict this curve through varying material interaction parameters using a romAI model.
- First, using HyperStudy, a Design of Experiments (DOE) is created with a select set of material interaction parameters.
- Through HST-EDEM coupling, EDEM simulation is triggered at set values of interaction parameters (following the DOE in the previous step).
- The response of the EDEM runs, which in this case is the temporal evolution of force and torque curves for each combination of Static Friction (SF) and Rolling Friction (RF) values, is recorded in a Comma-Separated Values (.CSV) file. This data is subsequently used to train a romAImodel.
- This 'trained' romAI model replaces EDEM within HyperStudy to predict material interaction parameters (SF and RF) for unfamiliar force and torque curves. The term 'unfamiliar' here refers to the fact that these curves were not parts of the training data.
The romAI generated model exhibits significantly faster computation speed than its EDEM counterpart. The higher computation speed is attributable to the data-driven approach of romAIrather than EDEM's physics-driven approach. The EDEM simulation for the FT4 Rheometer-based calibration test takes around 30 Mins to run (on NVIDIA RTX 2000 GPU), while the romAI model completes the same simulation in less than a minute.
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| Figure 1: Methodology for efficient material model calibration using romAI (a) train romAI using high-fidelity EDEM generated data, (b) substitute EDEM with trained romAI for calibration of the unknown material parameters |
Simulation Files and Workflow
The files associated with this article contains, EDEM deck for FT4 Rheometer, training and test data for romAI model(.CSV), HST archive file, and Twin Activate (.scm) file. These files can be downloaded here.
2.0 Generate training dataset with HyperStudy
The high-quality training data is obtained from a full factorial DOE of the input parameter space and a Modified Extensible Lattice Sequence (Mels). Using EDEM-HST coupling, EDEM is iteratively triggered at various combinations of input parameters, and the system's response, i.e., the evolution of force and torque on the rheometer blade during Basic Flowability Energy (BFE) test, is recorded. Figure 2 shows a HyperStudy session used to generate the training data.
In this work, the parameter space contains two variables, each with three levels. Thus, nine simulation runs are obtained from a full factorial DOE, and seven additional data points are gathered from Mels.
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| Figure 2: Using HyperStudy to generate high-fidelity training data through EDEM with a full-factorial DOE and Mels. |
Workflow for generating training data
After unzipping the downloaded files, EDEM deck can be triggered through HST for generation of training data. Navigate to folder 'HyperStudy_Synthetic_DataGeneration'. Using HyperStudy launch 'DataGeneration_HST_EDEM.hstx', right click on empty space under ‘Explorer’ tab and select ‘Add’. Under ‘select type’ use ‘DOE’ followed by ‘Definition From’ 
‘Setup’ 
‘OK’. A new DOE will be created in the ‘Explorer tab’. Within this new DOE, select ‘Specifications’ followed by ‘Mode’ and click ‘Apply’ and ‘Next’. Under ‘Evaluation Tasks’ click on ‘Evaluate Task’. This will run the EDEM deck at DOE-based parameter combination and provide the ‘BFE_Report.csv’. An already collated CSV file of the training data is provided with the attachment.
2.1 Training a romAI Model
The romAI can be accessed within Altair's Twin Activate, a unique block-diagram modeling environment. An important consideration while training a romAI model is limiting the noise within the training dataset. The noise, for the case of FT4 rheometer, can be attributed to the stochastic nature of the DEM-based particle simulation. This is achieved through the romAI's data filtering functionality. Training the model starts with importing the filtered data (Figure 3(a)), defining the model’s architecture, and specifying the training parameters (hyperparameters) (Figure 3(b)). Upon completion of training, the model is first evaluated for its prediction accuracy on the training set (Figure 3(c)). Each of these tasks is performed within the 'Pre-processor,' 'Builder,' and 'Post-processor' sections of the modeling interface. This allows for a systematic and easy-to-use workflow.
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| Figure 3: Workflow for training romAI model (a) Pre-processor for importing data, each segment is an output response for a given input variable(s), (b) Builder for defining training parameters, and (c) post-processing section to evaluate model's performance and accuracy. |
2.2 Utilization and validation of trained romAI model with HyperStudy
2.2.1 Setting up Twin Activate
A romAI model can be utilized from Twin Activate. Figure 4(a) marks the romAI model at the center as 
, the three inputs to this block are Static Friction (SF), Rolling Friction (RF), and the slope of the linearly decreasing height of the rheometer blade. These inputs are marked 
, 
, and 
, respectively. A CSV file marked 
, is used to record the force and torque curves as predicted by the romAI model. A sample clock marked 
, is used as an external activation to set the sampling period for the CSV block. The input height as well as the simulation time needs to be specified by the user in such a way that it matches the physical test’s height-time curve, as shown in Figure 4(a) and Figure 4(c), respectively. Having set this modeling workflow, the Twin Activate file is ready to be integrated into HyperStudy, serving as a replacement for EDEM for material model calibration.
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| Figure 4: (a) A romAI model setup within Twin Activate, |
Workflow for running the trained romAI model
In the provided files, navigate to the folder 'Activate_and_romAI'. Open ‘Rheometer.scm’ through Twin Activate. To run the romAI model for a set of friction coefficients click on ‘Model’ 
specify the value of ‘rf’ and ‘sf’ 
‘OK’. After clicking on ‘Run Simulation’, a ‘Rheometer_Out.csv’ would be generated (in the same folder containing ‘Rheometer.scm’).
2.2.2 Integrating Twin Activate to HyperStudy
Setup Definition
The Twin Activate model, as shown in Figure 4, can be linked to HyperStudy for efficient job management while leveraging the systematic design exploration capabilities of HyperStudy. To allow HyperStudy to execute a twin-activate model, ‘Activate_batch.bat’ is registered as a solver script, as illustrated in Figure 5(a) and Figure 5(b). Next, the Twin Activate model can be added to the setup definition.
Pointing to the 'Rheometer.scm' file (accompanying this article) within HyperStudy exposes the input parameters used within the Activate model, described in section 2.2.1 (shown in Figure 4(b)). These are the input variables that HyperStudy can alter to achieve a user-specified goal. Upon each successful execution of the 'Rheometer.scm' file, a corresponding 'Rheometer_out.csv' file is created that contains the force and torque curves corresponding to the set rolling and static friction values.
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| Figure 5: Workflow for registering Twin Activate file to HyperStudy (a) register solver script, (b) path pointing to activate batch file in the installation folder, and (c) defining setup definition with HyperStudy |
Define Output Response
Considering a well-trained romAI model, two sets of force and torque curves exist. One set is predicted by the romAI model, termed 'Reference Curve,' shown in blue in Figure 6, and another is generated by physical measurements, termed 'Target Curve,' shown in red in Figure 6. The objective of HyperStudy is to minimize the area difference between these two curves. This is accomplished by triggering the romAI model at various combinations of input variables and comparing the output against the set target curve. Here, we can observe that the set of input variables, as predicted by romAI, that best minimizes the area difference is similar (within a tolerance) to those used in EDEM to generate the target curve. This confirms the predictive capabilities of the romAI® model. To further improve the optimization, an additional constraint that tries to match the maximum torque value of the reference curve to the target curve is added to the output response in HST.
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| Figure 6: Defining output response in HyperStudy® with an objective to minimize the area difference between the target and the reference curves |
Testing and validation
Two sets of target curves are used to validate the romAI model, as shown in Figures 7(a) and Figure 7(b). These curves are representative of physical measurements. Using HyperStudy’s Global Response Search Method (GRSM); the romAI model is tasked to chase the target curve (minimizing the area difference between target and reference curves) by altering friction coefficients for each iteration, as shown in Figure 7. Once the optimization process is complete, the suggested values of input variables (by romAI) are compared against the actual (EDEM) values. An excellent agreement between the two can be observed for the two test cases, as shown in Figure 7. While the optimization runs suggest several acceptable solutions, the comparison is made for the ones that best minimize the area difference between the torque curves.
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| Figure 7: Validation of the romAI® model against two test parameters foreign to the training dataset |
Workflow
To view the test runs, navigate to folder 'HyperStudy_romAI_based_Calibration'. Two HST archive files are provided with the download (SF_0.25_RF_0.25.hstx and SF_0.65_RF_0.75.hstx). These files can be launched using HyperStudy.
3.0 Conclusion
Attributing to an iterative approach of material model calibration, arriving at material interaction parameters that best match experimental tests is a computationally intensive task. The higher the number of variables to be calibrated, the more expensive the calibration would be.
Using romAI in material model calibration for DEM studies offers a significant reduction in computational time with reasonably high accuracy. The model is easy to set up with training data gathered through previous simulations or through a DOE-based approach. A well-trained model can subsequently be used for effective calibration with minimal iterations or provide insight into bounds within which one can expect optima.
While this article focused on the use of FT4 rheometer as an example, a similar approach can be extended to other calibration tests.
Further Readings and Resources
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| 5. | Digital twins for Oral Solid Dose manufacturing process: Webinar |
| 6. | EDEM Material Modelling: 4 steps to accelerate your learning curve! |